In-Place Determination of Reservoir Relative Permeability Using Well Test Analysis

Abstract

Abstract This paper describes a new method to estimate two- and three-phase relative permeabilities in-situ, using pressure transient analysis. The technique requires a short drawdown test, consisting of a number of steps of increasing flow rate. The resulting relative permeabilities reflect the properties of the whole drainage area, rather than those of a small laboratory core. The proposed technique is a major improvement over current historical performance methods. These existing methods need data over long periods, yet only cover a range of saturation up to present conditions – all future projections require extrapolation. By contrast, the new method estimates relative permeabilities at sandface saturations, which cover a range of future reservoir conditions. The well test can be repeated at a later stage of depletion to forecast still further into the future. The proposed technique applies the solutions of multiphase diffusivity equation in terms of the pseudopressure function, m(p). These solutions have already been reported for constant rate tests in solution gas-drive reservoirs. This paper extends the pseudopressure solutions to three-phase systems. Two- and three-phase solutions are then superposed to obtain multiple-rate solutions, the basis for two- and three-phase relative permeability equations. A saturation equation developed originally by Bϕe et al. for solution gas-drive reservoirs, is also extended here to three-phase reservoirs. These pressure-saturation equations can be used to estimate sandface saturations during the test. Using a commercial black-oil simulator, example well tests were simulated over a 40% range in gas saturation. Both two- and three-phase results show close agreement with input relative permeability curves. In cases where relative permeability is not homogeneous within the drainage area, the resulting estimates of relative permeability curves were very representative of in-situ heterogeneities. The proposed technique offers a means to estimate two- and three-phase relative permeabilities at in-situ reservoir conditions, accounting for heterogeneities, wettability and fluid composition. It also seems to be the most appropriate way to obtain estimates for subsequent reservoir engineering analysis.